Rényi entropies for one-dimensional quantum systems with mixed boundary conditions
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
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2023
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| author | Estienne, Benoit Ikhlef, Yacine Rotaru, Andrei |
| author_facet | Estienne, Benoit Ikhlef, Yacine Rotaru, Andrei |
| contents | We present a general method for calculating Rényi entropies in the ground state of a one-dimensional critical system with mixed open boundaries, for an interval starting at one of its ends. In the conformal field theory framework, this computation boils down to the evaluation of the correlation function of one twist field and two boundary condition changing operators in the cyclic orbifold. Exploiting null-vectors of the cyclic orbifold, we derive ordinary differential equations satisfied by these correlation functions. In particular, we obtain an explicit expression for the second Rényi entropy valid for any diagonal minimal model, but with a particular set of mixed boundary conditions. In order to compare our results with numerical data for the Ising and three-state Potts critical chains, we also identify and compute the leading finite size corrections. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2301_02124 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Rényi entropies for one-dimensional quantum systems with mixed boundary conditions Estienne, Benoit Ikhlef, Yacine Rotaru, Andrei Statistical Mechanics High Energy Physics - Theory Mathematical Physics We present a general method for calculating Rényi entropies in the ground state of a one-dimensional critical system with mixed open boundaries, for an interval starting at one of its ends. In the conformal field theory framework, this computation boils down to the evaluation of the correlation function of one twist field and two boundary condition changing operators in the cyclic orbifold. Exploiting null-vectors of the cyclic orbifold, we derive ordinary differential equations satisfied by these correlation functions. In particular, we obtain an explicit expression for the second Rényi entropy valid for any diagonal minimal model, but with a particular set of mixed boundary conditions. In order to compare our results with numerical data for the Ising and three-state Potts critical chains, we also identify and compute the leading finite size corrections. |
| title | Rényi entropies for one-dimensional quantum systems with mixed boundary conditions |
| topic | Statistical Mechanics High Energy Physics - Theory Mathematical Physics |
| url | https://arxiv.org/abs/2301.02124 |